ARCH/GARCH Models

78 Pages·2017·3.73 MB·English

by  Wei Zhu

ARCH/GARCH Models
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Risk Management
— Risk: the quantifiable likelihood of loss or less-than-expected
returns.
— In recent decades the field of financial risk management has
undergone explosive development.
— Risk management has been described as “one of the most
important innovations of the 20th century”.
— But risk management is not something new.
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Risk Management
José (Joseph) De La Vega was a
Jewish merchant and poet residing
in 17th century Amsterdam.
There was a discussion between a
lawyer, a trader and a philosopher
in his book Confusion of
Confusions.
Their discussion contains what we
now recognize as European options
and a description of their use for
risk management.
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Risk Management
— There are three major risk types:
— market risk: the risk of a change in the value of a financial
position due to changes in the value of the underlying assets.
— credit risk: the risk of not receiving promised repayments
on outstanding investments.
— operational risk: the risk of losses resulting from inadequate
or failed internal processes, people and systems, or from
external events.
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Risk Management
— VaR (Value at Risk), introduced by JPMorgan in the 1980s,
is probably the most widely used risk measure in financial
institutions.
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Risk Management
— Given some confidence level 𝛼 ∈ 0,1 . The VaR of our
portfolio at the confidence level α is given by the smallest
value 𝑙 such that the probability that the loss 𝐿 exceeds 𝑙 is
no larger than 𝛼.
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VaR
The steps to calculate
σ
t
days to be
market Volatility
forecasted
position measure
VAR
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Level of confidence Report of potential
loss
The success of VaR
Is a result of the method used to estimate the
risk
The certainty of the report depends upon the
volatility
type of model used to compute the
on which these forecast is based
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Volatility
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Volatility
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